Simplify (x^2-36)/(x^2+4x-12)

$\frac{x^{2} - 36}{x^{2} + 4 x - 12}$

Step 1

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 6^{2}}{x^{2} + 4 x - 12}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 6$ .

$\frac{(x + 6) (x - 6)}{x^{2} + 4 x - 12}$

Step 2

Factor $x^{2} + 4 x - 12$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $4$ .

$- 2, 6$

Write the factored form using these integers.

$\frac{(x + 6) (x - 6)}{(x - 2) (x + 6)}$

Step 3

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{(x + 6) (x - 6)}{(x - 2) (x + 6)}$

Rewrite the expression.

$\frac{x - 6}{x - 2}$

Simplify (x^2-36)/(x^2+4x-12)

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